In communication systems including transmitters and receivers, antenna array beamforming provides increased signal quality (high directional antenna beamforming gain) and an extended communication range by steering the transmitted signal in a narrow direction. For this reason, such beamforming has been widely adopted in radar, sonar and other communication systems.
Antenna training approaches have been proposed for transmit and receive beamforming with one-dimensional operations. However, such training approaches cannot be applied or used for multiple dimension beamforming (multi-beamforming, also known as transmit precoding).